To be able to formulate and apply basic notions,  concepts, methods of mathematical control theory. 

Lecture, discussion, examples

The main goal of this lecture course is to introduce fundamental concepts of mathematical control theory, offering valuable tools for the analysis and design of control systems. The following topics will be considered:LINEAR SYSTEMS:Controllability  (Kalman rank condition, Kalman decomposition, Brunovsky canonical form)Stabilizability (Elements of Lyapunov stability theory, necessary and sufficient stabilziability conditions)Observability (Kalman observability criterion, Luenberger observer)ELEMENTS OF NONLINEAR SYSTEMS:Elements of geometric control theory (controllability rank condition, Chow–Rashevskii theorem)Stabilziation of nonlinear systemsELEMENTS OF OPTIMAL CONTROL THEORYThe above theoretical concepts will be accompanied by practical examples, such as control of mechanical systems, parking problem, etc.

Necessary: Analysis, Linear Algebra, Desirable: Ordinary Differential Equations and/or System Theory

H. Khalil. Nonlinear Systems.H. Nijmeijer , A. van der Schaft.  Nonlinear Dynamical Control Systems.E.D. Sontag. Mathematical control theory. 

Written end-term exam. The exam takes place in writing and consists of a theoretical and a practical parts. The total durations is about 90-120 minutes. 

Contents of the course.  Theoretical part: definitions, theorems, proofs.Practical part: exercises.

In order to pass the exam, at least 50% of the points (from both parts in total) must be achieved.